# CH07 - CHAPTER 7 1 Assume that the one-period spot interest...

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CHAPTER 7 1. Assume that the one-period spot interest rate is 3 percent and the two-period spot interest rate is 6 percent. Answer the following questions: (a) What is the present value of \$100 received one year from now? (b) What is the present value of \$100 received two years from now? (c) You are going to receive \$100 two years from now. What is its time 1 value? What is the forward interest rate? (d) Suppose you invest \$1 today at the two-period spot interest rate; what is its value at time 2? Alternatively you invest \$1 at the one-period spot rate and reinvest at the forward interest rate; what is the value at time 2? How do these two investments compare? R 0,1 = 3% R 0,2 = 6% a. \$97.09 = 1.03 100 = PV b. \$89.00 = ) (1.06 100 = PV 2 c. (1 + R 0,2 ) 2 = (1 + R 0,1 )(1 + f 0,2 ) (1 + 0.06) 2 = (1.03)(1 + f 0,2 ) f 0,2 = 9.087% Time 1 value = 01 . 1 9 \$ = 1.0909 100 d. 1(1 + R 0,2 ) 2 = 1(1+ 0.06) 2 = \$1.12 1(1 + R 0,1 )(1 + f 0,2 ) = 1(1.03)(1.0909) = \$1.12 2. Treasury strips with \$100 par values have the following prices: one-period, \$90; two- period, \$80. Answer the following questions: (a) What are the one-period and two-period spot interest rates? (b) What is the forward interest rate? (c) If you invest \$1 in one-period strips, what is the value after one period? (d) If you invest \$1 in two-period strips, what is the value after two periods? (e) If you invest \$1 at time 1 at the forward interest rate implied by the strips, what is the value of this dollar at time 2?

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a. 11.11% = R R + 1 100 = 90 0,1 0,1 11.80% = R ) R + (1 100 = 80 0,2 2 0,2 b. (1 + R 0,2 ) 2 = (1 + R 0,1 )(1 + f 0,2 ) (1.1180) 2 = (1.1111)(1 + f 0,2 ) f 0,2 = 12.50% c. 1(1.1111) = \$1.11 d. 1(1.1180) 2 = \$1.25 e. 1(1.1250) = \$1.1250 3. Treasury strips with \$100 par values have the following prices: one-period, \$94; two- period, \$87. You are going to receive an annuity of \$100 for the next two periods. What is the present value of this annuity? What is the time 1 value of this annuity? What is the time 2 value of this annuity? PVA = (100)(0.94) + (100)(.87) = \$181.00
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CH07 - CHAPTER 7 1 Assume that the one-period spot interest...

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